Inference of ground surface temperature history from subsurface temperature data: Interpreting ensembles of borehole logs

Ground surface temperature histories (GSTHs) inferred from borehole temperature-depth (T-z) data are often degraded, to a various extent, by random or systematic noise in the T-z data and in the measurements of thermophysical properties of the earth. To minimize the effects of noise, and hence improve the fidelity of the inferred GSTH, a plausible approach is to perform a simultaneous inversion of the T-z logs in a region, or alternatively, to invert the individual T-z logs and then average the resulting GSTHs. Averaging and simultaneous inversion are conceptually different: whereas an averaging can always be peformed, a simultaneous inversion is predicated on the assumption of a common transient component of the GSTH in all the T-z logs. In this work we examine and compare the two approaches, using a time domain inverse formulation based on the method of least squares. We consider a set of scenarios: (a) multiple T-z logs from a single borehole, (b) multiple boreholes from a single site, (c) multiple boreholes in similar climatological settings, and (d) multiple boreholes in different climatological settings. We show that for (a), (b) and (c), averaging and simultaneous inversion yield nearly identical results. For boreholes in different settings, the assumption of a common transient GSTH may be invalid and averaging and simultaneous inversion give divergent results.